Mixing
tangent distance between two handwritten digits
0
$begingroup$
Suppose we have two handwritten images "3"MNIST three and "6"MNIST six. The task is to compute the tangent distance between the two. An explanation at undergraduate level is highly appreciated.
tangent-spaces
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
$endgroup$
add a comment |
0
$begingroup$
Suppose we have two handwritten images "3"MNIST three and "6"MNIST six. The task is to compute the tangent distance between the two. An explanation at undergraduate level is highly appreciated.
tangent-spaces
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
$endgroup$
1
$begingroup$
What do you know about the topic so far? Do you know the definition of tangent distance?
$endgroup$
– Matti P.
Jan 22 at 10:38
$begingroup$
Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/…
$endgroup$
– Matti P.
Jan 22 at 10:41
$begingroup$
great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $alpha$ degrees around the center and the unrotated image (also as column vector) i.e., begin{equation} mathrm{boldsymbol{TV}} = mathcal{F}(boldsymbol{x}^prime; alpha) - boldsymbol{x}' end{equation} (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $alpha$ ?
$endgroup$
– Alexander K.
Jan 22 at 15:09
add a comment |
0
0
0
$begingroup$
Suppose we have two handwritten images "3"MNIST three and "6"MNIST six. The task is to compute the tangent distance between the two. An explanation at undergraduate level is highly appreciated.
tangent-spaces
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
$endgroup$
Suppose we have two handwritten images "3"MNIST three and "6"MNIST six. The task is to compute the tangent distance between the two. An explanation at undergraduate level is highly appreciated.
tangent-spaces
tangent-spaces
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
asked Jan 22 at 10:37
Alexander K.Alexander K.
1
1
1
$begingroup$
What do you know about the topic so far? Do you know the definition of tangent distance?
$endgroup$
– Matti P.
Jan 22 at 10:38
$begingroup$
Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/…
$endgroup$
– Matti P.
Jan 22 at 10:41
$begingroup$
great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $alpha$ degrees around the center and the unrotated image (also as column vector) i.e., begin{equation} mathrm{boldsymbol{TV}} = mathcal{F}(boldsymbol{x}^prime; alpha) - boldsymbol{x}' end{equation} (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $alpha$ ?
$endgroup$
– Alexander K.
Jan 22 at 15:09
add a comment |
1
$begingroup$
What do you know about the topic so far? Do you know the definition of tangent distance?
$endgroup$
– Matti P.
Jan 22 at 10:38
$begingroup$
Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/…
$endgroup$
– Matti P.
Jan 22 at 10:41
$begingroup$
great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $alpha$ degrees around the center and the unrotated image (also as column vector) i.e., begin{equation} mathrm{boldsymbol{TV}} = mathcal{F}(boldsymbol{x}^prime; alpha) - boldsymbol{x}' end{equation} (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $alpha$ ?
$endgroup$
– Alexander K.
Jan 22 at 15:09
1
1
$begingroup$
What do you know about the topic so far? Do you know the definition of tangent distance?
$endgroup$
– Matti P.
Jan 22 at 10:38
$begingroup$
What do you know about the topic so far? Do you know the definition of tangent distance?
$endgroup$
– Matti P.
Jan 22 at 10:38
$begingroup$
Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/…
$endgroup$
– Matti P.
Jan 22 at 10:41
$begingroup$
Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/…
$endgroup$
– Matti P.
Jan 22 at 10:41
$begingroup$
great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $alpha$ degrees around the center and the unrotated image (also as column vector) i.e., begin{equation} mathrm{boldsymbol{TV}} = mathcal{F}(boldsymbol{x}^prime; alpha) - boldsymbol{x}' end{equation} (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $alpha$ ?
$endgroup$
– Alexander K.
Jan 22 at 15:09
$begingroup$
great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $alpha$ degrees around the center and the unrotated image (also as column vector) i.e., begin{equation} mathrm{boldsymbol{TV}} = mathcal{F}(boldsymbol{x}^prime; alpha) - boldsymbol{x}' end{equation} (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $alpha$ ?
$endgroup$
– Alexander K.
Jan 22 at 15:09
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3082986%2ftangent-distance-between-two-handwritten-digits%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3082986%2ftangent-distance-between-two-handwritten-digits%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
What do you know about the topic so far? Do you know the definition of tangent distance?
$endgroup$
– Matti P.
Jan 22 at 10:38
$begingroup$
Here is something about the topic : cedar.buffalo.edu/~srihari/CSE555/…
$endgroup$
– Matti P.
Jan 22 at 10:41
$begingroup$
great slides. thank you. Suppose, we consider only rotation. Then the tangent vector $TV$ correspondes to the difference between the image $x'$ (as colomn vector) rotated $alpha$ degrees around the center and the unrotated image (also as column vector) i.e., begin{equation} mathrm{boldsymbol{TV}} = mathcal{F}(boldsymbol{x}^prime; alpha) - boldsymbol{x}' end{equation} (see slide 38). Is this correct? Do I have to compute the tangent vector for any rotation angle $alpha$ ?
$endgroup$
– Alexander K.
Jan 22 at 15:09